Abstract
The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a copper–water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. U. S. Choi and J. A. Eastman, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” in Proc. of the ASME Int. Mech. Eng. Congress and Exposition, San Francisco, November 12–17, 1995 (ASME, New York, 1995), FED V. 231/MD V. 66, pp. 99–105.
I. A. Kinloch, S. A. Roberts, and A. H. Windle, “A Rheological Study of Concentrated Aqueous Nanotube Dispersions,” Polymer 43, 7483–7491 (2002).
V. Tohver, A. Chan, O. Sakurada, and J. A. Lewis, “Nanoparticle Engineering of Complex Fluid Behaviour,” Langmuir 17, 8414–8421 (2001).
D. T. Wasan and A. D. Nikolov, “Spreading of Nanofluids on Solids,” Nature 423, 156–159 (2003).
L. J. Crane, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys. 21, 645–647 (1970).
P. S. Gupta and A. S. Gupta, “Heat and Mass Transfer on a Stretching Sheet with Suction and Blowing,” Canad. J. Chem. Eng. 55, 744–746 (1977).
C. Y. Wang, “Liquid Film on an Unsteady Stretching Sheet,” Quart. Appl. Math. 48, 601–610 (1990).
Miklavčič and C. Y. Wang, “Viscous Flow due a Shrinking Sheet,” Quart. Appl. Math. 64, 283–290 (2006).
E. Magyari and B. Keller, “Heat and Mass Transfer in the Boundary Layers on an Exponentially Stretching Continuous Surface,” J. Phys., D: Appl. Phys. 32, 577–585 (1999).
K. Bhattacharyya, “Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet,” Chinese Phys. Lett. 28, 074701 (2011).
W. A. Khan and I. Pop, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet,” Int. J. Heat Mass Transfer 53, 2477–2483 (2010).
S. Nadeem and C. Lee, “Boundary Layer Flow of Nanofluid Over an Exponentially Stretching Surface,” Nanoscale Res. Lett. 7, 94 (2012).
N. Bachok, A. Ishak, and I. Pop, “Stagnation-Point Flow Over a Stretching/Shrinking Sheet in a Nanofluid,” Nanoscale Res. Lett. 6, 623–633 (2011).
M. A. A. Hamad and M. Ferdows, “Similarity Solutions to Viscous Flow and Heat Transfer of Nanofluid over Nonlinearly Stretching Sheet,” Appl. Math. Mech. (English Ed.) 33, 923–930 (2012).
N. Bachok, A. Ishak, R. Nazar, and N. Senu, “Stagnation-Point Flow over a Permeable Stretching/Shrinking Sheet in a Copper–Water Nanofluid,” Boundary Value Problems 39, 1–10 (2013).
K. Das, “Mixed Convection Stagnation Point Flow and Heat Transfer of Cu–Water Nanofluids Towards a Shrinking Sheet,” Heat Transfer—Asian Res. 42, 230–242 (2013).
O. D. Makinde, W. A. Khan, and Z. H. Khan, “Buoyancy Effects on MHD Stagnation Point Flow and Heat Transfer of a Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet,” Int. J. Heat Mass Transfer 62, 526–533 (2013).
E. Haile and B. Shankar, “A Steady MHD Boundary-Layer Flow of Water-Based Nanofluids over a Moving Permeable Flat Plate,” Int. J. Math. Res. 4, 27–41 (2015).
K. Zaimi, A. Ishak, and I. Pop, “Boundary Layer Flow and Heat Transfer over a Nonlinearly Permeable Stretching/Shrinking Sheet in a Nanofluid,” Sci. Rep. 4, 4404 (2014).
T. G. Fang, J. Zhang, and S. S. Yao, “Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer,” Chinese Phys. Lett. 26, 014703 (2009).
J. H. Merkin and V. Kumaran, “The Unsteady MHD Boundary-Layer Flow on a Shrinking Sheet,” Eur. J. Mech., B: Fluids 29, 357–363 (2010).
N. A. Yacob, A. Ishak, and I. Pop, “Unsteady Flow of a Power-Law Fluid Past a Shrinking Sheet with Mass Transfer,” Z. Naturforsch. 67a, 65–69 (2012).
K. Bhattacharyya, “Heat Transfer Analysis in Unsteady Boundary Layer Stagnation-Point Flow Towards a Shrinking/Stretching Sheet,” Ain Shams Eng. J. 4, 259–264 (2013).
N. Bachok, A. Ishak, and I. Pop, “Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid over a Permeable Stretching/Shrinking Sheet,” Int. J. Heat Mass Transfer 55, 2102–2109 (2012).
R. Viskanta and R. J. Grosh, “Boundary Layer in Thermal Radiation Absorbing and Emitting Media,” Int. J. Heat Mass Transfer 5, 795–806 (1962).
D. Pal, “Heat and Mass Transfer in Stagnation-Point Flow Towards a Stretching Surface in the Presence of Buoyancy Force and Thermal Radiation,” Meccanica 44, 145–158 (2009).
K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer Towards a Shrinking Sheet,” Int. J. Heat Mass Transfer 54, 308–313 (2011).
S. Mukhopadhyay, K. Bhattacharyya, and G. C. Layek, “Steady Boundary Layer Flow and Heat Transfer over a Porous Moving Plate in Presence of Thermal Radiation,” Int. J. Heat Mass Transfer 54, 2751–2757 (2011).
K. Bhattacharyya, S. Mukhopadhyay, G. C. Layek, and I. Pop, “Effects of Thermal Radiation on Micropolar Fluid Flow and Heat Transfer over a Porous Shrinking Sheet,” Int. J. Heat Mass Transfer 55, 2945–2952 (2012).
S. Mukhopadhyay and R. S. R. Gorla, “Effects of Partial Slip on Boundary Layer Flow Past a Permeable Exponential Stretching Sheet in Presence of Thermal Radiation,” Heat Mass Transfer 48, 1773–1781 (2012).
S. Nadeem and R. U. Haq, “Effect of Thermal Radiation for Magnetohydrodynamic Boundary Layer Flow of a Nanofluid Past a Stretching Sheet with Convective Boundary Condition,” J. Comput. Theoret. Nanosci. 11, 1–9 (2014).
N. Bachok, A. Ishak, and I. Pop, “Boundary Layer Stagnation-Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in a Nanofluid,” Int. J. Heat Mass Transfer 55, 8122–8128 (2012).
H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” Int. J. Heat Fluid Flow 29, 1326–1336 (2008).
M. Q. Brewster, Thermal Radiative Transfer Properties (John Wiley and Sons, New York, 1972).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 58, No. 4, pp. 115–125, July–August, 2017.
Original Russian Text © M.S. Uddin, A. Zaib, K. Bhattacharyya.
Rights and permissions
About this article
Cite this article
Uddin, M.S., Zaib, A. & Bhattacharyya, K. Effect of thermal radiation on heat transfer in an unsteady copper–water nanofluid flow over an exponentially shrinking porous sheet. J Appl Mech Tech Phy 58, 670–678 (2017). https://doi.org/10.1134/S0021894417040113
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894417040113